crumbcloth

from The Century Dictionary.

• noun A cloth, chiefly of a stout kind of damask, laid under a table to receive falling fragments and keep the carpet or floor clean. It is often made to extend over the greater part of a dining-room floor.
• noun A stout kind of damask used for stair-coverings.

from the GNU version of the Collaborative International Dictionary of English.

• noun A cloth to be laid under a dining table to receive falling fragments, and keep the carpet or floor clean.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A cloth laid under a dining table to receive falling fragments and keep the carpet or floor clean.